You can store & run osu stable from an external drive (USB, CD, Phone's storage (USB)).
For a transfer I recommend the following:
- Songs (folder)
- Skins (folder)
- osu!.cfg
- osu!.{name}.cfg (config file, contains your settings)
(Name being your PC's name, not your osu username)
- collections.db (contains all your in-game collections)
- scores.db (contains all your local scores)
If used:
- Chat (folder)
- Replays (folder)
- Exports (folder)
Not sure if you want to keep them, but there also is the
Screenshots folder, which you can transfer.
Note: If the name of your old and new device are different, you will have to copy the contents of osu!.{name}.cfg into the new config manually for your settings to load correctly.
(The new osu!.{name}.cfg will be created after you've first started the game on the new device)
In regards to lazer I can't help you, I have not used this release enough to give any help on that.